Lecture 25

Learning objectives

After this class, you should be able to:

1. Given a sequence of n integers, a number k in [1,n], and a sequence of random numbers, show the steps involved in applying the good randomized selection algorithm discussed in class to find the k th smallest of these numbers.
2. Explain the idea behind the better randomized selection algorithm.
3. Prove the Markov and Chebyshev inequalities.

Reading assignment

1. Class notes and sections 3 and 4 of http://www.csee.wvu.edu/~ksmani/courses/fa01/random/lecnotes/lecture4.pdf.
2. Review statistics from Appendix A of the above URL.

Exercises and review questions

• Questions on current lecture's material
  1. (Post your answer on the discussion board) Give an example set of data and show how the better randomized selection algorithm that we discussed in class would determine the 4 th smallest number in it. Use a sequence of random numbers generated by any of the Unix random number generators, and show this sequence too.
  2. Give tight examples for Markov and Chebyshev inequalities.

• Questions on next lecture's material
  1. For independent random variables, prove that the expected value of the product is the product of expected values.